Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Value of Lim X → ∞ N ! ( N + 1 ) ! − N ! - Mathematics

MCQ

The value of \[\lim_{x \to \infty} \frac{n!}{\left( n + 1 \right)! - n!}\] 

Options

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  • none of these 

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Solution

\[\lim_{n \to \infty} \frac{n!}{\left( n + 1 \right)! - n!}\]
\[\text{ Dividing } N^r \text{ and } D^r \text{ by } n!: \]
\[ \lim_{n \to \infty} \frac{1}{\frac{\left( n + 1 \right)!}{n!} - 1}\]
\[ = \lim_{n \to \infty} \frac{1}{\frac{\left( n + 1 \right)n!}{n!} - 1}\]
\[ = \lim_{n \to \infty} \frac{1}{n + 1 - 1}\]
\[ = \lim_{n \to \infty} = \frac{1}{n} = 0\] 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 35 | Page 80
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